Super-critical Hardy--Littlewood inequalities for multilinear forms

D. Nunez-Alarcon; D. Paulino; D. Pellegrino

Super-critical Hardy--Littlewood inequalities for multilinear forms

Functional Analysis 2020-02-25 v1

Authors: D. Nunez-Alarcon , D. Paulino , D. Pellegrino

Abstract

The multilinear Hardy--Littlewood inequalities provide estimates for the sum of the coefficients of multilinear forms $T:\ell_{p_{1}}^{n}\times\cdots \times\ell_{p_{m}}^{n}\rightarrow\mathbb{R}$ (or $\mathbb{C}$ ) when $1/p_{1}+\cdots+1/p_{m}<1.$ In this paper we investigate the critical and super-critical cases; i.e., when $1/p_{1}+\cdots+1/p_{m}\geq1.$

Keywords

hardy-littlewood inequality multilinear forms super-critical case critical case lp spaces

Cite

@article{arxiv.2002.10239,
  title  = {Super-critical Hardy--Littlewood inequalities for multilinear forms},
  author = {D. Nunez-Alarcon and D. Paulino and D. Pellegrino},
  journal= {arXiv preprint arXiv:2002.10239},
  year   = {2020}
}

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